Sydney University Algebra Seminar

    University of Sydney

    School of Mathematics and Statistics

    Algebra Seminar

    Piotr Hajac
    Mathematisches Institut, Universitaet Muenchen, Germany

    Noncommutative geometry of algebraic bundles

    Friday 10th August, 12-1pm, Carslaw 375.

    Coalgebra-Galois extensions of noncommutative algebras are algebraic analogues of principal bundles. To any such an extension one can associate modules much as vector bundles are associated to principal bundles. We show the equivalence of the relative projectivity of coaugmented coalgebra-Galois extensions and existence of strong connections. Then we prove that modules associated to such extensions via finite dimensional corepresentations are finetely generated projective, and thus fit the formalism of the Chern-Connes pairing between K-theory and cyclic cohomology. As an example, we use the Chern-Connes pairing to define, and the Noncommutative Index Theorem to compute, the Chern numbers of algebraic line bundles associated to the q-deformed Hopf fibration.